1. Gravitational Fields
Topic 6.1

2. Gravitational Force
What are the variables that affect the gravitational force on an object?
It was found (discovered?)that :
Masses are attractive
Compare with:
Sir Issac Newton
(1642 –1727)
What are the major differences?

3. Newton’s Law of Universal Gravitation

4. Newton’s law of universal gravitation
For large objects like the earth, r is the distance to the centre of mass

5. Calculations using Newton’s law
What is the force of attraction between Andrei and Mike?
7.3 x 10-8 N
2 m
63kg ?
70kg ?

6. Force of gravity due to earth on Mike?
(Mike’s weight)
63kg ?
F = Gm1m2 = x x 63 x 6 x 1024 = N (= mg)
r2 (6400 x 103)2
R = 6400 km, m = 6 x 1024 kg

7. Force of gravity due to earth on Michael?
F = Gm1m2 = x x 63 x 6 x 1024 = N (= mg)
r2 (6400 x 103)2
In other words, for any planet;
g = Gmp
rp2

8. Gravitational field
An area or region where a mass feels a gravitational force is called a gravitational field.
The gravitational field strength at any point in space is defined as the force per unit mass (on a small test mass) at that point.
g = F/m (in N.kg-1)

9. Gravitational field around a point mass
If we have two masses m1 and m2 distance r apart
F = Gm1m2/r2
Looking at the force on m1 due to m2, F = gm1
F = Gm1m2/r2 = gm1
g (field due to m2) = Gm2/r2 m1 m2

10. Gravitational field around a point mass
I told you, for any planet;
g = Gmp
rp2
Don’t forget that for a non point mass, r is the distance to the centre of mass
If we have two masses m1 and m2 distance r apart
F = Gm1m2/r2
Looking at the force on m1 due to m2, F = gm1
F = Gm1m2/r2 = gm1
g (field due to m2) = Gm2/r2 m1 m2

11. Gravitational field
Gravitational field is a vector, and any calculations regarding fields (especially involving adding the fields from more than one mass) must use vector addition.
Field here due to both masses? m1 m2

12. Gravitational field
Gravitational field is a vector, and any calculations regarding fields (especially involving adding the fields from more than one mass) must use vector addition.
Field here due to both masses?
Field due to m1 m1 m2

13. Gravitational field
Gravitational field is a vector, and any calculations regarding fields (especially involving adding the fields from more than one mass) must use vector addition.
Field due to m2
Field due to m1 m1 m2

14. Gravitational field
Gravitational field is a vector, and any calculations regarding fields (especially involving adding the fields from more than one mass) must use vector addition.
Field due to m2
Field due to m1
Resultant Field m1 m2

15. Gravitational field patterns
A gravitational field can be represented by lines and arrows on a diagram, in a similar ways to magnetic field lines.

16. Gravitational field patterns
A gravitational field can be represented by lines and arrows on a diagram, in a similar ways to magnetic field lines.
The closer the lines are together, the stronger the force felt.
Note, gravity is ALWAYS attractive
This is an example of a radial field

17. Field around a charged metal sphere
E = 0 inside the sphere

18. Field around a uniform spherical mass

19. Field close to the earth’s surface
Uniform